1. ECEN 5817 Housekeeping update
For both on-campus and CAETE students: A DVD of recorded lectures from Professor Erickson’s Spring ’06 class will be mailed to you sometime next week. These will not be available on the CAETE website CUAnywhere.colorado.edu
For on-campus students: You will not have access to this semesters recorded lectures on the CAETE website
For CAETE students: By popular request, scanned and ed homework will be accepted provided the submissions meet the following requirements:
Black and white (no color, no grayscale)
200 – 300 dpi
All problems scanned into ONE PDF file for the whole assignment
PDF file is easy to read, easy to open, and easy to print

2. Chapter 19 Resonant Conversion
Introduction
19.1 Sinusoidal analysis of resonant converters
19.2 Examples
Series resonant converter
Parallel resonant converter
19.3 Soft switching
Zero current switching
Zero voltage switching
19.4 Load-dependent properties of resonant converters
Exact characteristics of the series and parallel resonant converters

3. Equivalent circuit of rectifier
Rectifier input port:
Fundamental components of current and voltage are sinusoids that are in phase
Hence rectifier presents a resistive load to tank network
Effective resistance Re is
Rectifier equivalent circuit
With a resistive load R, this becomes
Loss free resistor

4. 19.1.4 Solution of converter voltage conversion ratio M = V/Vg
Eliminate Re:

5. Conversion ratio M
So we have shown that the conversion ratio of a resonant converter, having switch and rectifier networks as in previous slides, is equal to the magnitude of the tank network transfer function. This transfer function is evaluated with the tank loaded by the effective rectifier input resistance Re.

6. 19.2.2 Subharmonic modes of the SRC
Example: excitation of tank by third harmonic of switching frequency
Can now approximate vs(t) by its third harmonic:
Result of analysis:

7. Subharmonic modes of SRC
Not often used - reduced switch utilization and decreased voltage conversion ratio
Still need to be aware their existence

8. 19.2 Examples 19.2.1 Series resonant converter

9. Model: series resonant converter

10. Construction of Zi – Resonant (high Q) case C = 0
Construction of Zi – Resonant (high Q) case C = 0.1 μF, L = 1 mH, Re = 10 Ω

11. Construction of H = V / Vg – Resonant (high Q) case C = 0
Construction of H = V / Vg – Resonant (high Q) case C = 0.1 μF, L = 1 mH, Re = 10 Ω
Buck characteristic

12. Construction of Zi

13. Construction of H

14. Model: series resonant converter

15. Construction of Zi – Non-resonant (low Q) case C = 0
Construction of Zi – Non-resonant (low Q) case C = 0.1 μF, L = 1 mH, Re = 1 kΩ

16. Construction of H – Non-resonant (low Q) case C = 0
Construction of H – Non-resonant (low Q) case C = 0.1 μF, L = 1 mH, Re = 1 kΩ

17. 19.2.3 Parallel resonant dc-dc converter
Differs from series resonant converter as follows:
Different tank network
Rectifier is driven by sinusoidal voltage, and is connected to inductive-input low-pass filter
Need a new model for rectifier and filter networks

18. Model of uncontrolled rectifier with inductive filter network – input port
Fundamental component of iR(t):

19. Model of uncontrolled rectifier with inductive filter network – output port
Output inductor volt second balance: dc voltage is equal to average rectified tank output voltage

20. Effective resistance Re
Again define
In steady state, the dc output voltage V is equal to the average value of | vR |:
For a resistive load, V = IR. The effective resistance Re can then be expressed

21. Equivalent circuit model of uncontrolled rectifier with inductive filter network
Dependent voltage source based on rectified tank voltage.
Vs. SRC, dependent current source based on rectified tank current.

22. Equivalent circuit model Parallel resonant dc-dc converter

23. 2 different ways to construct transfer function H

24. Construction of Zi – Resonant (high Q) case C = 0
Construction of Zi – Resonant (high Q) case C = 0.1 μF, L = 1 mH, Re = 1 kΩ

25. Construction of H = V / Vg – Resonant (high Q) case C = 0
Construction of H = V / Vg – Resonant (high Q) case C = 0.1 μF, L = 1 mH, Re = 1 kΩ
Buck-boost characteristic

26. Construction of Zo

27. Construction of H

28. Dc conversion ratio of the PRC
At resonance, this becomes
PRC can step up the voltage, provided R > R0
PRC can produce M approaching infinity, provided output current is limited to value less than Vg / R0

29. Comparison of approximate and exact characteristics
Series resonant converter
Below resonance:
0.5 < F < 1
Above resonance:
1 < F

30. Comparison of approximate and exact characteristics
Parallel resonant converter
Exact equation:
solid lines
Sinusoidal approximation: shaded lines